gcse mathematics - st edmund campion catholic …...name for edexcel gcse mathematics paper 3c...

NameFor Edexcel

GCSE MathematicsPaper 3C (Non-Calculator)

Higher TierTime: 1 hour and 45 minutes

Materials requiredRuler, protractor, compasses,pen, pencil, eraser.Tracing paper may be used.

Instructions and Information for CandidatesWrite your name in the box at the top of the page.Answer all the questions in the spaces provided in this question paper.The marks for each question and for each part of a question are shown in brackets.The total number of marks for this paper is 100. There are 23 questions in this paper.Calculators must not be used.

Advice to CandidatesShow all stages in any calculation.Work steadily through the paper. Do not spend too long on one question.If you cannot answer a question, leave it and attempt the next one.Return at the end to those you have left out.

Written by Shaun ArmstrongOnly to be copied for use in the purchaser's school or college

EH3C © Churchill Maths Limited

GCSE Mathematics

Formulae: Higher Tier

Volume of a prism = area of cross section × length

Volume of sphere = 43 πr3 Volume of cone = 1

3 πr2hSurface area of sphere = 4πr2 Curved surface area of cone = πrl

In any triangle ABC The Quadratic EquationThe solutions of ax2 + bx + c = 0where a ≠ 0, are given by

x = −b±b2−4ac 2a

Sine Rule asin A =

bsin B =

csinC

Cosine Rule a2 = b2 + c2 – 2bc cos A

Area of triangle = 12 ab sin C


sectioncross

length

rl h

r

c B

C

A

b a

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Q1

Answer ALL TWENTY THREE questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

You must NOT use a calculator.

1. Fiona and Javed are doing a project on pets.

(a) Fiona writes a questionnaire for people who own a cat.

This is one of her questions.

“Is your cat

an indoor cat a short-haired cat a playful cat ”

Write down one way in which this is not a good question.

………………………………………………………………………………………

………………………………………………………………………………………

………………………………………………………………………………………(1)

(b) Javed wants to find out how often people who own a dog take it for a walk.

Design a suitable question he could use.You should include response boxes.

(2)(Total 3 marks)


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Q2

2. (a) Write down the inequality represented by the following diagram.

–4 –3 –2 –1 0 1 2 3 4 x

…………………………(1)

(b) Solve the inequality

4x + 3 < 15

…………………………(2)

(Total 3 marks)


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Q3

A C

B

8 cm

6 cm

8 cm

A C

3. Diagram NOTaccurately drawn

The diagram shows a sketch of an isosceles triangle, ABC.AB = BC = 8 cm.AC = 6 cm.

(a) Make an accurate drawing of triangle ABC.The side AC has been drawn for you.You must show all your construction lines.

(2)

(b) Measure the size of angle ABC on your diagram.°

……………………… (1)

(Total 3 marks)


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Q4

4. Students in Class P and Class Q complete the same homework.The two-way table shows information about the grades the students were given.

(a) Complete the two-way table.

(3)

A student is picked at random from Class Q.

(b) Write down the probability that the student got a Grade C on the homework.

………………………(2)

A student is picked at random from all those that got a Grade A on the homework.

(c) Write down the probability that the student is in Class Q.

………………………(1)

(Total 6 marks)


Grade A Grade CGrade B Total

Total

Class Q

Class P 8

24 23

7

4 30

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Q5

30°

50°

y

x

A

CB

D

H

z

EFG

52°

5. (a) Diagram NOTaccurately drawn

The lines AB and CD are parallel.

(i) Write down the size of the angle marked x.°

……………………

(ii) Find the size of the angle marked y.°

…………………… (3)

(b) Diagram NOTaccurately drawn

EFG is a straight line and EH = FH = FG.Angle EHF = 52°.

Find the size of the angle marked z.

°……………………

(3)(Total 6 marks)


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Q6

6.

(a) Reflect the shaded rectangle in the y-axis.Label this image A.

(2)

(b) Rotate the shaded rectangle 180° about O.Label this image B.

(2)(Total 4 marks)


1 2 43 5 x

y

–2 –1 6

–3

–2

1

2

4

3

5

–1

–5

–4

O–5 –4 –3

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Q7

2 64 8 10 12

CumulativeFrequency

Age in years

10

30

20

40

O

7. This cumulative frequency graph shows information about the ages of 40 cars.

Use the graph to estimate

(a) the median age of the cars,

……………………… years(1)

(b) the percentage of the cars that are more than 3 years old.

……………………… %(3)

(Total 4 marks)


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Q8

Q9

8. y = x 5x − 3

(a) Work out the value of y when x = 4.

y = …………………(2)

(b) Work out the value of x when y = 2.

x = …………………(3)

(Total 5 marks)

9.

A company buys 16 computer monitors for £3464

Work out the cost of each monitor.

£ ………………………

(Total 3 marks)


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Q10

Q11

10. (a) Solve 6x – 7 = 17

x = ……………………(2)

(b) Solve y 1

5 + 2 y 1

2 = 1

y = ……………………(4)

(Total 6 marks)

11. (a) Work out 58 + 5

6

Give your answer as a fraction in its simplest form.

……………………(2)

(b) Work out 79 ÷ 1

3

Give your answer as a fraction in its simplest form.

……………………(3)

(Total 5 marks)


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Q12

4 cm

6 cm

8 cm


The diagram shows the net of a triangular prism.

Calculate the volume of the prism that can be formed from this net.State the units of your answer.

………………………………

(Total 4 marks)


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Q13

Q14

13. Here are some expressions.

a + 2c b + 2π ab + c2 a(b + c)

2πb3 c + 2 ab(c + 2) 2b(a2 + c2 )

a, b and c represent lengths.π and 2 are numbers which have no dimensions.

Write down one of the expressions above which could be

(a) a length,…………………………

(1)

(b) an area,…………………………

(1)

(c) a volume.…………………………

(1)(Total 3 marks)

14. (a) Write 200 in standard form.

…………………………(1)

(b) Write 3 × 10–6 as an ordinary number.

…………………………(1)

(c) Work out

(5 × 106) × (7 × 105)

Give your answer in standard form.

…………………………(2)

(Total 4 marks)


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Q15

A

C

E

B

D

4 cm

10 cm


ABCD is a square.ADE is a triangle.AE = 4cm.DE = 10 cm.Angle AED = 90°.

Work out the area of pentagon ABCDE.

………………………… cm2

(Total 4 marks)


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Q16

16. Exton College has 420 students in year 12.This is 5% more than last year.

Rhona says

“You can work out the number of year 12 students last year by calculating 0.95 × 420”.

(a) Explain why Rhona is wrong.

………………………………………………………………………………………

………………………………………………………………………………………(1)

(b) Work out the number of students in year 12 last year.

………………………(3)

(Total 4 marks)


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Q17

17. Solve the simultaneous equations

y = 2x2

y = 5x + 3

x = …………………… y = ……………………

or x = …………………… y = ……………………

(Total 4 marks)


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Q18

18. In this question you may use the grid provided below but you are not required to do so.

The locus of the point P is such that the distance of P from the point (1, 0) is equal to the distance of P from the point (5, 0).

(a) Find an equation for the locus of P.

……………………………(2)

The locus of the point Q is such that the distance of Q from the point (3, 1) is equal to the distance of Q from the point (6, –2).

(b) Find an equation for the locus of Q.

……………………………(3)

(Total 5 marks)


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Q19

Q20

19. (a) Evaluate

(i) 490

……………………

(ii) 4912

……………………(2)

(b) Write 20 in the form k 5, where k is an integer.

……………………(2)

(Total 4 marks)

20. M is inversely proportional to f.

When f = 3, M = 14.

Find the value of f when M = 6.

f = ……………………

(Total 5 marks)


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Q21

A

C

x

B 3x – 9


Angle ABC = 90°.AB = x cm.BC = 3x – 9 cm.

The area of triangle ABC is 15 cm2.

(a) Show that x2 – 3x – 10 = 0

(3)

(b) (i) Solve the equation x2 – 3x – 10 = 0

x = …………… or x = ……………

(ii) Hence find the length of BC.

…………………… cm(3)

(Total 6 marks)


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Q22

20 40 8060 100

1

2

3

Frequencydensity

(kicks per metre)

Distance (d m)

O

22. The histogram gives information about the distance, in metres, of 100 goalkicks.

Use the histogram to complete the table.

Distance (d m) Frequency

0 ≤ d < 40

40 ≤ d < 60

60 ≤ d < 70

70 ≤ d < 80

80 ≤ d < 100

(Total 3 marks)


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Q23

P

A

Q BO

R

S


OAB is a triangle.P lies on OA such that OP : OA = 1 : 3Q lies on OB such that OQ : OB = 1 : 3

OP = p and OQ = q.

(a) Find, in terms of p and q, the vectors

(i) OA…………………………

(ii) AB

…………………………(2)

R and S lie on AB such AR = RS = SB.

(b) Prove that PR and QS are parallel.

(4)(Total 6 marks)

TOTAL FOR PAPER: 100 MARKS

END


gcse mathematics - st edmund campion catholic …...name for edexcel gcse mathematics paper 3c...

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